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The binomial theorem worksheets Grades 11–12

Expand binomials and find terms with the binomial theorem.

The front of the free the binomial theorem worksheet
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Free · Worked example · 18 problems · Answer key · US Letter

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How to do it

The coefficients of (a + b)ⁿ are row n of Pascal's triangle, nC0 to nCn. The powers of a go down while the powers of b go up.

(3x−3)4=(3x)4+4(3x)3(−3)+6(3x)2(−3)2+4(3x)(−3)3+(−3)4(3x - 3)^{4} = (3x)^{4} + 4(3x)^{3}(-3) + 6(3x)^{2}(-3)^{2} + 4(3x)(-3)^{3} + (-3)^{4}row 4 of Pascal's triangle: 1, 4, 6, 4, 1
(3x)4+4(3x)3(−3)+6(3x)2(−3)2+4(3x)(−3)3+(−3)4=81x4−324x3+486x2−324x+81(3x)^{4} + 4(3x)^{3}(-3) + 6(3x)^{2}(-3)^{2} + 4(3x)(-3)^{3} + (-3)^{4} = 81x^{4} - 324x^{3} + 486x^{2} - 324x + 81multiply out each term

Example problems

  1. (x+1)5:the x term=(x + 1)^{5}:\quad \text{the }x\ \text{term} =
  2. (x−2)5:the x term=(x - 2)^{5}:\quad \text{the }x\ \text{term} =
  3. (2x−1)4:the x term=(2x - 1)^{4}:\quad \text{the }x\ \text{term} =
  4. (3x+2)3=(3x + 2)^{3} =

Sequences and series

  1. Arithmetic sequences
  2. Geometric sequences
  3. Writing the formula for a sequence
  4. Sigma notation
  5. Arithmetic series
  6. Geometric series
  7. Infinite geometric series
  8. Combinations (nCk)
  9. The binomial theorem